distributed-quantum-error-correction

name

distributed-quantum-error-correction

description

Design and analyze distributed quantum error correction (QEC) systems using bivariate bicycle (BB) codes in modular quantum computing architectures. Covers qLDPC code partitioning across multiple processors, star network topology for inter-processor connectivity, BP+OSD decoding, and fault tolerance threshold analysis under circuit-level noise. Use when: designing modular quantum computers, implementing distributed QEC, partitioning qLDPC codes across processors, analyzing inter-processor entanglement overhead, or studying BB codes for trapped-ion/neutral-atom platforms.

Distributed Quantum Error Correction

Overview

Bivariate bicycle (BB) codes — a class of quantum LDPC codes — offer higher encoding rates than surface codes but require long-range stabilizer connections impractical on monolithic nearest-neighbor devices. The solution: partition qubits across modular processors linked by shared Bell pairs.

Key Concepts

BB Codes (qLDPC)

• [[144,12,12]] BB code: 144 physical qubits, 12 logical qubits, distance 12
• Encoding rate k/n ≈ 0.083 vs surface code k/n ≈ 1/(2d²)
• Long-range stabilizers require non-local connectivity

Modular Architecture

• Partition qubits across N processors (4, 6, or 12 typical)
• Each processor: all-to-all internal connectivity (trapped-ion, neutral-atom)
• Inter-processor links: shared Bell pairs via star network
• Nonlocal gate noise scaling factor β relative to local gates

Star Network Topology

    Processor 1 ──┐
    Processor 2 ──┼── Central Hub (shared Bell pair generation)
    Processor 3 ──┤
    ...          ──┘

Decoding Pipeline

1. Syndrome extraction via stabilizer measurements
2. BP+OSD (Belief Propagation + Ordered Statistics Decoding)
3. Monte Carlo simulation for logical error rate estimation
4. Pseudo-threshold analysis across noise parameters

Design Workflow

Step 1: Code Selection

Choose qLDPC code parameters [[n,k,d]] based on target logical error rate and hardware constraints. BB codes offer superior rate-distance tradeoffs.

Step 2: Partitioning Strategy

Partition n physical qubits across P processors:

• Minimize inter-processor stabilizer crossings
• Balance qubit count per processor (n/P each)
• Ensure each processor's internal connectivity supports local stabilizers

Step 3: Inter-Processor Connectivity

• Use star network for Bell pair distribution
• Model inter-processor noise as β × local_noise_rate
• β typically 5-100× higher depending on link technology

Step 4: Threshold Analysis

Vary physical error rate p and noise scaling β to map:

• Pseudo-threshold curves for each processor count
• Logical error rate vs physical error rate
• Scaling behavior as P increases

Critical Design Considerations

1. Inter-processor overhead: Each stabilizer crossing requires a Bell pair
2. β sensitivity: Performance degrades sharply when β > 10 for surface-level noise; BB codes tolerate higher β due to sparse stabilizer structure
3. Processor count tradeoff: More processors → smaller chips but more inter-processor crossings
4. Decoding complexity: BP+OSD scales O(n·polylog(n)) vs O(n²) for MWPM

Activation Keywords

• distributed quantum error correction
• modular quantum computing
• qLDPC codes
• bivariate bicycle codes
• BB code
• quantum error correction architecture
• multi-processor quantum computer
• star network quantum
• BP+OSD decoding
• quantum fault tolerance
• 分布式量子纠错
• 模块化量子计算

Related Concepts

• Surface codes (planar, nearest-neighbor only)
• Trapped-ion quantum computing (all-to-all connectivity)
• Neutral-atom quantum computing (reconfigurable connectivity)
• Quantum LDPC codes (qLDPC)
• Circuit-level noise models
• Fault-tolerant quantum computation (FTQC)

References

• arXiv:2605.04663 — Distributed Quantum Error Correction with Bivariate Bicycle Codes in a Modular Architecture